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Nov. 12, 2010 The concept of entropy was introduced into ergodic theory by

Summary: David Kerr
Texas A&M
Nov. 12, 2010
3:30 p.m.
CL 408
The concept of entropy was introduced into ergodic theory by
Kolmogorov in the late 1950s. It can be viewed as a measure of the
average information gained in learning that the orbit of an unidentified
point visits a certain sequence of sets in a given partition of the space.
This dynamical version of Shannon's information-theoretic entropy
revolutionize the study of measure-preserving actions, which until then
had relied on invariants of a spectral, as opposed to combinatorial,
nature. Entropy theory as originally conceived by Kolmogorov was
ultimately seen to apply most generally to actions of amenable groups,
for which one can average over partial orbits in a way that produces a
dynamical invariant.
Very recently Lewis Bowen showed, quite surprisingly, that the theory of
measure entropy can be vastly extended to the realm of actions of


Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina


Collections: Mathematics